Measuring frequency domain granger causality for multiple blocks of interacting time series

Area of Science:

• Neuroscience
• Time Series Analysis
• Network Science

Background:

• Existing frequency-domain causality measures, such as Geweke's feedback measures, directed coherence (DC), and partial directed coherence (PDC), are limited in analyzing complex neural systems.
• These measures often rely on simplifying assumptions about the structure of time series data, restricting their application to specific scenarios.

Purpose of the Study:

• To unify and generalize existing frequency-domain causality measures.
• To propose novel causality measures, block DC (bDC) and block PDC (bPDC), for analyzing multiple blocks of time series.
• To extend causality analysis to vector-valued processes and capture internal dependencies within these processes.

Main Methods:

• Developed block DC (bDC) and block PDC (bPDC) measures, unifying and extending existing approaches.
• Introduced logarithmic counterparts, multivariate total feedback and direct feedback, within a multivariate framework.
• Conducted theoretical analysis to verify desirable properties and capabilities of the new measures.

Main Results:

• The proposed measures (bDC, bPDC, etc.) can distinguish between direct and total causality between time series blocks.
• These measures generalize existing methods, reducing to DC, PDC, and Geweke's measures in specific cases.
• Numerical analyses demonstrated efficient estimation from short time series and improved accuracy in detecting frequency-domain causality.

Conclusions:

• The novel block causality measures offer a unified and generalized framework for analyzing directional connectivity in neural systems.
• These measures accurately capture complex interactions within and between multiple time series blocks, including internal dependencies.
• The proposed methods are suitable for neurophysiological applications involving simultaneous recording of brain activity signals from multiple regions.